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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 685 · 40 sums
TalentJR

The trick (Ekadhikena Purvena): 2, 5, 10: the last digit (even; 0 or 5; 0). 3 and 9: add the digits. 4: the last two digits. 8: the last three digits. 6: even and passes the rule for 3. 11: from the right, add the 1st, 3rd, 5th… digits and the 2nd, 4th… digits; the difference must be 0 or a multiple of 11. Any prime p: multiply p by 1, 3, 7 or 9 so it ends in 9; one more than the digits before the 9 is the osculator (7 → 5, 13 → 4, 17 → 12, 19 → 2, 23 → 7, 29 → 3). Take the last digit × the osculator and add it to the rest; repeat until the number is small and check the times table. Composite numbers: split into two factors that share no factor and pass BOTH rules — 6 = 2 × 3, 12 = 3 × 4, 15 = 3 × 5, 18 = 2 × 9, 20 = 4 × 5, 24 = 3 × 8, 30 = 3 × 10.

NameDateTime takenScore ___ / 40
  1. 1.Is 12243 divisible by 7?
  2. 2.Is 126265 divisible by 23?
  3. 3.Is 32570 divisible by 10?
  4. 4.Is 70763 divisible by 11?
  5. 5.Is 31138 divisible by 5?
  6. 6.Is 155164 divisible by 23?
  7. 7.Is 36657 divisible by 9?
  8. 8.Is 52272 divisible by 23?
  9. 9.Is 19840 divisible by 4?
  10. 10.Is 949 divisible by 6?
  11. 11.Is 45024 divisible by 12?
  12. 12.Is 23448 divisible by 4?
  13. 13.Is 15016 divisible by 4?
  14. 14.Is 116533 divisible by 24?
  15. 15.Is 20677 divisible by 3?
  16. 16.Is 34680 divisible by 6?
  17. 17.Is 16987 divisible by 3?
  18. 18.Is 72020 divisible by 20?
  19. 19.Is 63470 divisible by 23?
  20. 20.Is 1824 divisible by 2?
  21. 21.Is 94700 divisible by 24?
  22. 22.Is 49452 divisible by 19?
  23. 23.Is 112781 divisible by 23?
  24. 24.Is 8090 divisible by 5?
  25. 25.Is 10520 divisible by 8?
  26. 26.Is 59502 divisible by 13?
  27. 27.Is 62192 divisible by 13?
  28. 28.Is 11986 divisible by 2?
  29. 29.Is 37224 divisible by 24?
  30. 30.Is 80222 divisible by 15?
  31. 31.Is 1484 divisible by 18?
  32. 32.Is 159819 divisible by 29?
  33. 33.Is 117864 divisible by 19?
  34. 34.Is 82914 divisible by 19?
  35. 35.Is 55418 divisible by 11?
  36. 36.Is 15963 divisible by 7?
  37. 37.Is 51960 divisible by 20?
  38. 38.Is 68222 divisible by 13?
  39. 39.Is 15500 divisible by 4?
  40. 40.Is 71133 divisible by 11?

Answer key

  1. yes
  2. no
  3. yes
  4. yes
  5. no
  6. no
  7. yes
  8. no
  9. yes
  10. no
  11. yes
  12. yes
  13. yes
  14. no
  15. no
  16. yes
  17. no
  18. yes
  19. no
  20. yes
  21. no
  22. no
  23. no
  24. yes
  25. yes
  26. no
  27. yes
  28. yes
  29. yes
  30. no
  31. no
  32. yes
  33. no
  34. no
  35. yes
  36. no
  37. yes
  38. no
  39. yes
  40. no

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